Electron. J. Diff. Eqns., Vol. 2000(2000), No. 63, pp. 1-28.

Neumann and periodic boundary-value problems for quasilinear ordinary differential equations with a nonlinearity in the derivative

Petr Girg

We present sufficient conditions for the existence of solutions to Neumann and periodic boundary-value problems for some class of quasilinear ordinary differential equations. We also show that this condition is necessary for certain nonlinearities. Our results involve the p-Laplacian, the mean-curvature operator and nonlinearities blowing up.

Submitted July 18, 2000. Published October 16, 2000.
Math Subject Classifications: 34B15, 47H12.
Key Words: p-Laplacian, Leray-Schauder degree, Landesmann-Lazer condition.

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Petr Girg
Department of Mathematics
University of West Bohemia
P. O. Box 314
306 14 Plzen, Czech Republic
e-mail: pgirg@kma.zcu.cz

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